Course Overview

Introduction

This course covers fundamental concepts in electricity, magnetism, optics, and modern physics. Key topics include electric and magnetic forces, electric fields and potentials, DC circuits, electromagnetic waves, optics, quantum mechanics, atomic models, and nuclear physics.

• Electricity: Electric force, electric field and potential, electric currents, DC circuits, and circuit devices.

• Magnetism: Magnetic force and magnetic field.

• Electricity and Magnetism Combined: Magnetic fields and electric currents, electromagnetic waves, light, optics (mirrors and lenses).

• Modern Physics: Wave nature of matter, photoelectric effect, quantum mechanics, Bohr model of the atom, nuclear physics (radioactivity, fission, fusion).

Chapter 16: Electric Charge and Coulomb’s Law

The Origin of Electricity

The electrical nature of matter is inherent in atomic structure. Atoms are composed of protons, neutrons, and electrons, each with specific masses and charges.

• Proton mass:

• Neutron mass:

• Electron mass:

• Elementary charge: (Coulomb is the SI unit of charge)

In nature, atoms are electrically neutral, containing equal numbers of protons and electrons. By adding or removing electrons, matter acquires a net electric charge:

• Charge quantization: where is the number of electrons added or removed.

Example: Number of Electrons in One Coulomb

How many electrons are in one coulomb of negative charge?

• electrons

• This is an extremely large number, comparable to the number of stars in 100 million Milky Way galaxies.

Charged Objects and the Electric Force

Electric charge can be transferred between objects, typically by moving electrons (which are more mobile than protons).

• The object that loses electrons becomes positively charged.

• The object that gains electrons becomes negatively charged.

Law of Conservation of Electric Charge

The net electric charge of an isolated system remains constant during any process (charge is conserved).

Attraction and Repulsion

• Like charges repel each other.

• Unlike charges attract each other.

Conductors, Insulators, and Semiconductors

Electric charge can exist on an object and can also move through an object, depending on the material's properties.

• Electrical Conductors: Substances that readily conduct electric charge (e.g., metals such as copper, aluminum, gold).

• Electrical Insulators: Materials that conduct electric charge poorly (e.g., glass, plastics, rubber).

• Semiconductors: Materials with conductivity between conductors and insulators (e.g., silicon, germanium, gallium-arsenide).

Charging by Contact and by Induction

• Charging by Contact: Direct transfer of electrons from one object to another by touching.

• Charging by Induction: Redistribution of charges in an object caused by the influence of a nearby charged object, without direct contact. Grounding may be used to allow electrons to enter or leave the object.

Electroscope

An electroscope is a device used to detect electric charge. The gold-leaf electroscope, invented in the 1700s, demonstrates the presence of charge by the repulsion of gold leaves.

Polarization

A negatively charged rod can induce a slight positive surface charge on a nearby insulator (e.g., plastic) by polarizing its molecules.

Coulomb’s Law

Coulomb’s Law quantifies the electrostatic force between two point charges. The force is proportional to the product of the charges and inversely proportional to the square of the distance between them.

• Coulomb’s Law: where and is the distance between charges.

• Permittivity of free space:

• Relation to Newton’s Law of Gravitation:

• The forces are equal in magnitude and opposite in direction (Newton’s 3rd law).

Example: Bohr Model of the Hydrogen Atom

In the Bohr model, the electron orbits the proton at a fixed radius. The electrostatic force provides the centripetal force for circular motion.

• For , ,

• Speed of electron: (about 1% of the speed of light)

Example: Three Charges on a Line

To find the net force on a charge due to two other charges, calculate the individual forces using Coulomb’s Law and add them vectorially.

• For , , at specified distances:

• Net force:

Example: Three Charges in Two Dimensions

When charges are arranged in two dimensions, resolve the forces into components and use vector addition.

• ,

• Resolve into and components, sum, and find magnitude and direction:

• ,

• ,

Summary Table: Types of Materials and Their Electrical Properties

Additional info: The notes above expand on the provided slides by including definitions, formulas, and step-by-step examples for clarity and completeness.